Prove that
using Bromwich's integral
Prove that using Bromwich's integral 3 = t- e-t/2, 8+1 sen(t) -1 a) 2 (s2+s+1)} -...
4. Use the Laplace integral formula to find (b) L-1 T"e (5-1) s2(s 1) 0 4. Use the Laplace integral formula to find (b) L-1 T"e (5-1) s2(s 1) 0
1. Evaluate the indefinite integral sen (2x) – 7 cos(9x) – sec°(3x) dx = 2. Evaluate the indefinite integral | cor(3x) – sec(x) tant(x) + 9 tan(2x) dx = 3. Calculate the indefinite integral using the substitution rule | sec?0 tan*o do =
Evaluate the integral -SX cos(x-ve dv dx. Select one: S-1 s(s+1) 1 O b. (s2-1)(s+1) S $3-2+s-1 C 1 O d. $3-$2+5-1 O e. stights+1 S 33+2+3+1 1 f. ܕܨܨܠܨ 53 +52 ++1 S (s2-1)(s-1) 1 (s2-1)(3+1) O h.
Solve the Integral cos" dx Rpta. 2 (cosa cosa »" (senc +6 2 sen
8, Prove that if R is an integral domain and a E R such that a2 + 2a + 1-0 then a =-1. Then give an example of a ring that is not an integral domain for which a2a 1-0 but a f -1. 8, Prove that if R is an integral domain and a E R such that a2 + 2a + 1-0 then a =-1. Then give an example of a ring that is not an integral domain...
1.) 2.) 3.) Identify f(t) for the function F(s) 8(+ 2)(8 + 3) s(s + 2)(s + 4) Multiple Choice (3.00+ 2.00e-2t-3.00e-4540 4.00u(t+ 2.00e-2t+3.00e-4t O (3.00 + 2.00e-2t +3.00e-44 3.00u(t) +2.00 e e-2t+4.00e-4 Find f(t) for the function F(s) = 32- 8s + 4 (s + 1)(8 + 2)2 Multiple Choice O 29=-24e-t+ (-12) -2t *+(-24)te-27 О = (13e-t +(-12)e-2t + (-24)te-21) (1) + O 10 = (13e-*+(-24)e-2 +(-12)te-210 80 = 8e-T+(-12)e-2t + (-24)te-2t Identify f(t) for the function F...
2. For n . define functions T inductivelv such that 0, 1, 2, . . . (cosx) = cos(nx), with Folz) 1. (a) Prove that Tn is a polynomial for every n and compute its degree. b) Prove the recursion formula (c) Compute the integral dr 山 for every n, m E N 2. For n . define functions T inductivelv such that 0, 1, 2, . . . (cosx) = cos(nx), with Folz) 1. (a) Prove that Tn is...
Sin and Cos V15 13. Si sen(a) y está en el cuadrante III entonces sen 10 10 I. B. C.- 4 D. 4 4 14. cos(10")cos(59) + sen(10°)sen (5) = A) sen(5) B) cos(15) C) -cos(5) D) cos(59) 15. _1 + cot-(t) - csc (t) = A) 1 B) 4 C) 0 D) -1 16. 3 sen(x) + 2 sen(x + 2) = A) 5 sen(x) B) -5 sen(x) C) 5 sen(x) + 1 D) 5 sen(x) + 2
5) Using the table, find the Laplace inverse of S-3 F(s) = s2 - 2s + 4 Do not use line (16) in the table. Elementary Laplace Transforms Y(s) = LF0) = {e=f(e)dt 0 f(t) = ('{F(s)) F(s) = {f} f(t) = ('{F(s)} F(s) = {f} 1. 1 12. uct) -CS S> 0 S> 0 2. 1 S-a -F(s) 13. ue(t)f(t-c) S> a 3. th, nez* n! 14. ectf(t) F(s-c) S>0 s+ 14. t", p>-1 r(p+1) 15. f(ct) S> 0...
Change variables under the Laplace integral to prove that for a fixed τ, L{x(t−τ)}=e^(−sτ) X(s)